Here's how King Arthur Flour says to accomplish this. I think it looks fabulous.
http://www.kingarthurflour.com/blog/2012/12/07/brooklyn-style-cheesecake-the-dairy-dairy-best/
I'm having trouble imagining how the yellow cake is not going to come out totally squashed and maybe gummy. Unless the cheesecake part is particularly light and airy?
I know to bake the cake forst and then put in bottom of springform pan. but should I line it with parchement paper first? how do I get the cheesecake off the paper and on to a serving platter once cooled?
Although I haven't specifically done this with cheesecake, I've done it with regular cake: With a pencil, trace around the circumference of the springform-pan bottom with a pencil. Enlarge this circle all around by AT LEAST as much as the pan is high, if that makes sense (that is, pencil in a 9" circle if that is the diameter of your pan; if it is 2" high at the sides, add at least that amount all around the circle=at least 13" for the final circle. Cut it out. With scissors or kitchen shears, slash all around, at about 1-to 1-1/2 inch intervals, each slash reaching just to the inner circle. Fit it into the cake pan; the vertical segments will go up the sides of the pan, overlapping each other. Neaten the segments up carefully. We hope that since they overlap so well, no cheesecake batter will seep between the segments; you probably want to butter (and flour?? not sure about that part; perhaps you could use amaretto crumbs or the like) the pan to avoid the leakage problem. After baking, allow to cool, releasing the spring as directed by the recipe. I'm wondering if you should chill the cheesecake (or freeze). Pull down the sections of paper carefully, remove by folding softly and easing and shimmying it under the cake, little by little. I have a very large bench-scraper like "peel" for moving cake layers. You can use this to transfer the cheesecake portion and center it over the sponge.
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http://www.kingarthurflour.com/blog/2012/12/07/brooklyn-style-cheesecake-the-dairy-dairy-best/